Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, k\neq 0$. $\dfrac{{(p)^{-1}}}{{(pk^{-3})^{-4}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p}$ to the exponent ${-1}$ . Now ${1 \times -1 = -1}$ , so ${(p)^{-1} = p^{-1}}$ In the denominator, we can use the distributive property of exponents. ${(pk^{-3})^{-4} = (p)^{-4}(k^{-3})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p)^{-1}}}{{(pk^{-3})^{-4}}} = \dfrac{{p^{-1}}}{{p^{-4}k^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-1}}}{{p^{-4}k^{12}}} = \dfrac{{p^{-1}}}{{p^{-4}}} \cdot \dfrac{{1}}{{k^{12}}} = p^{{-1} - {(-4)}} \cdot k^{- {12}} = p^{3}k^{-12}$.